In this paper, a novel motion estimation (ME) scheme with efficient memory design is presented for the mobile multimedia applications in H.264/AVC. To obtain the optimal memory usage and achieve better coding quality under volatile system operating conditions, we propose a novel bandwidth-rate-distortion (B-R-D) algorithm by exploring the motion activity properties of various video sequences. This scheme allocates the optimized data bandwidth into the corresponding coded block in a rate distortion sense using the convex optimization approach. The experimental results indicate that our proposed B-R-D ME algorithm can achieve up to 71% bandwidth savings for CIF-size video.